Please use this identifier to cite or link to this item: doi:10.22028/D291-26259
Title: Stochastic processes in terms of inner premeasures
Author(s): König, Heinz
Language: English
Year of Publication: 2004
Free key words: Wiener process
Poisson process
maximal inner extensions
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: In a recent paper the author used his work in measure and integration to obtain the projective limit theorem of Kolmogorov in a comprehensive version in terms of inner premeasures. In the present paper the issue is the influence of the new theorem on the notion of stochastic processes. It leads to essential improvements in the foundation of special processes, of the Wiener process in the previous paper and of the Poisson process in the present one. But it also forms the basis for a natural redefinition of the entire notion. The stochastic processes in the reformed sense are in one-to-one correspondence with the traditional ones in case that the state space is a Polish topological space with its Borel \sigma algebra, but the sizes and procedures are quite different. The present approach makes an old idea of Kakutani come true, but with due adaptations.
Link to this record: urn:nbn:de:bsz:291-scidok-44630
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 105
Date of registration: 12-Jan-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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